We then obtain, from (77). 



- y u-|^ dT = I y u^ dx = u^ 



U dx 



But, by (73) and (78), 



j y dx = J y dx - J y dx = 1^ - i^ J (u^-u) dS 

 ^' BLW if *A 



Then, by (74) , 



- J ^^ '^^ = 4? [_^- J ^"r^) 



dS 



(81) 



Hence, by (73) and (81), (72) becomes 



D„ = - P 



J (u,-u)(Uq+u^) dS+^ 



(82) 



A formula for the viscous drag D can now be obtained by subtracting 

 the expression for D in (71) from that for D in (70) and then substituting 

 for D from (82) . Observing that the resulting integrand is nonzero only 

 over the wake area A, we obtain the result 



D = 



P/ 



^ j [2g(H -H)+(u^-u)(u^+u-2u^)+v^+w^-v^^-w^^] dS (83) 

 u, J. 



"o 



31 



